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Theorem nfs1v 1919
 Description: 𝑥 is not free in [𝑦 / 𝑥]𝜑 when 𝑥 and 𝑦 are distinct. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfs1v 𝑥[𝑦 / 𝑥]𝜑
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfs1v
StepHypRef Expression
1 hbs1 1918 . 2 ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)
21nfi 1442 1 𝑥[𝑦 / 𝑥]𝜑
 Colors of variables: wff set class Syntax hints:  Ⅎwnf 1440  [wsb 1742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743 This theorem is referenced by:  nfsbxy  1922  nfsbxyt  1923  sbco3v  1949  sbcomxyyz  1952  sbnf2  1961  mo2n  2034  mo23  2047  mor  2048  clelab  2283  cbvralf  2674  cbvrexf  2675  cbvralsv  2694  cbvrexsv  2695  cbvrab  2710  sbhypf  2761  mob2  2892  reu2  2900  sbcralt  3013  sbcrext  3014  sbcralg  3015  sbcreug  3017  sbcel12g  3046  sbceqg  3047  cbvreucsf  3095  cbvrabcsf  3096  disjiun  3960  cbvopab1  4037  cbvopab1s  4039  csbopabg  4042  cbvmptf  4058  cbvmpt  4059  opelopabsb  4219  frind  4311  tfis  4540  findes  4560  opeliunxp  4638  ralxpf  4729  rexxpf  4730  cbviota  5137  csbiotag  5160  isarep1  5253  cbvriota  5784  csbriotag  5786  abrexex2g  6062  abrexex2  6066  dfoprab4f  6135  finexdc  6840  ssfirab  6871  uzind4s  9484  zsupcllemstep  11813  bezoutlemmain  11862  cbvrald  13321  bj-bdfindes  13483  bj-findes  13515
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